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All sources NASA NTRS DOE OSTI

DOE OSTI2023

Bi-fidelity modeling of uncertain and partially unknown systems using DeepONets

Recent advances in modeling large-scale, complex physical systems have shifted research focuses towards data-driven techniques. However, generating datasets by simulating complex systems can require significant computational resources. Similarly, acquiring experimental datasets can prove difficult. For these systems, often computationally inexpensive, but in general inaccurate models, known as the low-fidelity models, are available. Here in this paper, we propose a bi-fidelity modeling approach for complex physical systems, where we model the discrepancy between the true system's response and a low-fidelity response in the presence of a small training dataset from the true system's response using a deep operator network, a neural network architecture suitable for approximating nonlinear operators. We apply the approach to systems that have parametric uncertainty and are partially unknown. Three numerical examples are used to show the efficacy of the proposed approach to model uncertain and partially unknown physical systems.

MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Closed-Form Approximation of the Total Variation Proximal Operator

Total variation (TV) is a widely used function for regularizing imaging inverse problems that is particularly appropriate for images whose underlying structure is piecewise constant. TV regularized optimization problems are typically solved using proximal methods, but the way in which they are applied is constrained by the absence of a closed-form expression for the proximal operator of the TV function. A closed-form approximation of the TV proximal operator has previously been proposed, but its accuracy was not theoretically explored in detail. Here, we address this gap by making several new theoretical contributions, proving that the approximation leads to a proximal operator of some convex function, it is equivalent to a gradient descent step on a smoothed version of TV, and that its error can be fully characterized and controlled with its scaling parameter. We experimentally validate our theoretical results on image denoising and sparse-view computed tomography (CT) image reconstruction.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2011

Optical Navigation for Dawn at Vesta

The Dawn S/C, launched in September 2007, towards Vesta and Ceres, will enter into orbit about asteroid Vesta in July 2011 and will conduct science remote sensing operations for approximately one year at various orbital altitudes. Vesta navigation operations begin with early approach in May 2011 until departure to Ceres in July 2012. A key navigation aspect is optical navigation, which will be conducted at all mission phases. Here we review the optical navigation plan, imaging, methodology, data types, as well as expected performance in the context of the overall mission navigation. A key aspect of optical navigation at Dawn that will receive particular attention is the extensive use of landmark navigation during most of mission phases. In addition to supporting real-time navigation operations, optical navigation will be used to determine some key physical characteristics of Vesta, such as the asteroid's pole & shape, to assist mission design & science operations.

Vesta↗

DOE OSTI2021

Non-intrusive nonlinear model reduction via machine learning approximations to low-dimensional operators

Abstract Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing such a reduced-order model typically requires significant modifications to the underlying simulation code. To address this, we propose a method that enables traditionally intrusive reduced-order models to be accurately approximated in a non-intrusive manner. Specifically, the approach approximates the low-dimensional operators associated with projection-based reduced-order models (ROMs) using modern machine-learning regression techniques. The only requirement of the simulation code is the ability to export the velocity given the state and parameters; this functionality is used to train the approximated low-dimensional operators. In addition to enabling nonintrusivity, we demonstrate that the approach also leads to very low computational complexity, achieving up to $$10^3{\times }$$ 10 3 × in run time. We demonstrate the effectiveness of the proposed technique on two types of PDEs. The domain of applications include both parabolic and hyperbolic PDEs, regardless of the dimension of full-order models (FOMs).

42 ENGINEERING↗

DOE OSTI2023

DeepONet-grid-UQ: A trustworthy deep operator framework for predicting the power grid’s post-fault trajectories

This paper proposes a novel data-driven method for the reliable prediction of the power grid’s post-fault trajectories, i.e., the power grid’s dynamic response after a disturbance or fault. Here, the proposed method is based on the recently proposed concept of Deep Operator Networks (DeepONets). Unlike traditional neural networks that learn to approximate functions, DeepONets are designed to approximate nonlinear operators, i.e., mappings between infinite-dimensional spaces. Under this operator framework, we design a novel and efficient DeepONet that (i) takes as inputs the trajectories collected before and during the fault and (ii) outputs the predicted post-fault trajectories. In addition, we endow our method with the much-needed ability to balance efficiency with reliable/trustworthy predictions via uncertainty quantification. To this end, we propose and compare two novel methods that enable quantifying the predictive uncertainty. First, we propose a Bayesian DeepONet (B-DeepONet) that uses stochastic gradient Hamiltonian Monte-Carlo to sample from the posterior distribution of the DeepONet trainable parameters. Then, we design a Probabilistic DeepONet (Prob-DeepONet) that uses a probabilistic training strategy to enable quantifying uncertainty at virtually no extra computational cost. Finally, we validate the proposed methods’ predictive power and uncertainty quantification capability using the New York-New England power grid model.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Generalized moving least squares vs. radial basis function finite difference methods for approximating surface derivatives

Approximating differential operators defined on two-dimensional surfaces is an important problem that arises in many areas of science and engineering. Over the past ten years, localized meshfree methods based on generalized moving least squares (GMLS) and radial basis function finite differences (RBF-FD) have been shown to be effective for this task as they can give high orders of accuracy at low computational cost, and they can be applied to surfaces defined only by point clouds. However, there have yet to be any studies that perform a direct comparison of these methods for approximating surface differential operators (SDOs). The first purpose of this work is to fill that gap. For this comparison, we focus on an RBF-FD method based on polyharmonic spline kernels and polynomials (PHS+Poly) since they are most closely related to the GMLS method. Additionally, we use a relatively new technique for approximating SDOs with RBF-FD called the tangent plane method since it is simpler than previous techniques and natural to use with PHS+Poly RBF-FD. Further, the second purpose of this work is to relate the tangent plane formulation of SDOs to the local coordinate formulation used in GMLS and to show that they are equivalent when the tangent space to the surface is known exactly. The final purpose is to use ideas from the GMLS SDO formulation to derive a new RBF-FD method for approximating the tangent space for a point cloud surface when it is unknown. For the numerical comparisons of the methods, we examine their convergence rates for approximating the surface gradient, divergence, and Laplacian as the point clouds are refined for various parameter choices. We also compare their efficiency in terms of accuracy per computational cost, both when including and excluding setup costs.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

Improving Estimation of the Koopman Operator with Kolmogorov–Smirnov Indicator Functions

It has become common to perform kinetic analysis using approximate Koopman operators that transform high-dimensional timeseries of observables into ranked dynamical modes. The key to the practical success of the approach is the identification of a set of observables that form a good basis on which to expand the slow relaxation modes. Good observables are, however, difficult to identify a priori and suboptimal choices can lead to significant underestimations of characteristic time scales. Leveraging the representation of slow dynamics in terms of Hidden Markov Models (HMM), we propose a simple and computationally efficient clustering procedure to infer surrogate observables that form a good basis for slow modes. Here, we apply the approach to an analytically solvable model system as well as on three protein systems of different complexities. We consistently demonstrate that the inferred indicator functions can significantly improve the estimation of the leading eigenvalues of Koopman operators and correctly identify key states and transition time scales of stochastic systems, even when good observables are not known a priori.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Bayesian, Multifidelity Operator Learning for Complex Engineering Systems–A Position Paper

Abstract Deep learning has significantly improved the state-of-the-art in computer vision and natural language processing, and holds great potential to design effective tools for predicting and simulating complex engineering systems. In particular, scientific machine learning seeks to apply the power of deep learning to scientific and engineering tasks, with operator learning (OL) emerging as a particularly effective tool. OL can approximate nonlinear operators arising in complex engineering systems, making it useful for simulating, designing, and controlling those systems. In this position paper, we provide a comprehensive overview of OL, including its potential applications to complex engineering domains. We cover three variations of OL approaches: deterministic OL for modeling nonautonomous systems, OL with uncertainty quantification (UQ) capabilities, and multifidelity OL. For each variation, we discuss drawbacks and potential applications to engineering, in addition to providing a detailed explanation. We also highlight how multifidelity OL approaches with UQ capabilities can be used to design, optimize, and control engineering systems. Finally, we outline some potential challenges for OL within the engineering domain.

Computer Science↗

DOE OSTI2021

A Convex Data-Driven Approach for Nonlinear Control Synthesis

We consider a class of nonlinear control synthesis problems where the underlying mathematical models are not explicitly known. We propose a data-driven approach to stabilize the systems when only sample trajectories of the dynamics are accessible. Our method is built on the density-function-based stability certificate that is the dual to the Lyapunov function for dynamic systems. Unlike Lyapunov-based methods, density functions lead to a convex formulation for a joint search of the control strategy and the stability certificate. This type of convex problem can be solved efficiently using the machinery of the sum of squares (SOS). For the data-driven part, we exploit the fact that the duality results in the stability theory can be understood through the lens of Perron–Frobenius and Koopman operators. This allows us to use data-driven methods to approximate these operators and combine them with the SOS techniques to establish a convex formulation of control synthesis. The efficacy of the proposed approach is demonstrated through several examples.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1999

Computation of Steady and Unsteady Laminar Flames: Theory

In this paper we describe the numerical analysis underlying our efforts to develop an accurate and reliable code for simulating flame propagation using complex physical and chemical models. We discuss our spatial and temporal discretization schemes, which in our current implementations range in order from two to six. In space we use staggered meshes to define discrete divergence and gradient operators, allowing us to approximate complex diffusion operators while maintaining ellipticity. Our temporal discretization is based on the use of preconditioning to produce a highly efficient linearly implicit method with good stability properties. High order for time accurate simulations is obtained through the use of extrapolation or deferred correction procedures. We also discuss our techniques for computing stationary flames. The primary issue here is the automatic generation of initial approximations for the application of Newton's method. We use a novel time-stepping procedure, which allows the dynamic updating of the flame speed and forces the flame front towards a specified location. Numerical experiments are presented, primarily for the stationary flame problem. These illustrate the reliability of our techniques, and the dependence of the results on various code parameters.

Hagstrom, Thomas↗

NASA NTRS1990

The Liquid Annular Reactor System (LARS) propulsion

A concept for very high specific impulse (greater than 2000 seconds) direct nuclear propulsion is described. The concept, termed the liquid annular reactor system (LARS), uses liquid nuclear fuel elements to heat hydrogen propellant to very high temperatures (approximately 6000 K). Operating pressure is moderate (approximately 10 atm), with the result that the outlet hydrogen is virtually 100 percent dissociated to monatomic H. The molten fuel is contained in a solid container of its own material, which is rotated to stabilize the liquid layer by centripetal force. LARS reactor designs are described, together with neutronic and thermal-hydraulic analyses. Power levels are on the order of 200 megawatts. Typically, LARS designs use seven rotating fuel elements, are beryllium moderated, and have critical radii of approximately 100 cm (core L/D approximately equal to 1.5).

Powell, James↗

NASA NTRS2014

Deployable Fresnel Rings

Deployable Fresnel rings (DFRs) significantly enhance the realizable gain of an antenna. This innovation is intended to be used in combination with another antenna element, as the DFR itself acts as a focusing or microwave lens element for a primary antenna. This method is completely passive, and is also completely wireless in that it requires neither a cable, nor a connector from the antenna port of the primary antenna to the DFR. The technology improves upon the previous NASA technology called a Tri-Sector Deployable Array Antenna in at least three critical aspects. In contrast to the previous technology, this innovation requires no connector, cable, or other physical interface to the primary communication radio or sensor device. The achievable improvement in terms of antenna gain is significantly higher than has been achieved with the previous technology. Also, where previous embodiments of the Tri-Sector antenna have been constructed with combinations of conventional (e.g., printed circuit board) and conductive fabric materials, this innovation is realized using only conductive and non-conductive fabric (i.e., "e-textile") materials, with the possible exception of a spring-like deployment ring. Conceptually, a DFR operates by canceling the out-of-phase radiation at a plane by insertion of a conducting ring or rings of a specific size and distance from the source antenna, defined by Fresnel zones. Design of DFRs follow similar procedures to those outlined for conventional Fresnel zone rings. Gain enhancement using a single ring is verified experimentally and through computational simulation. The experimental test setup involves a microstrip patch antenna that is directly behind a single-ring DFR and is radiating towards a second microstrip patch antenna. The first patch antenna and DFR are shown. At 2.42 GHz, the DFR improves the transmit antenna gain by 8.6 dB, as shown in Figure 2, relative to the wireless link without the DFR. A figure illustrates the relative strength of power coupling between the first and second microstrip antennas with and without the DFR. Typically, a DFR is designed for use at a particular frequency; however, testing of a DFR indicated a relatively wide operational bandwidth of approximately 8.2%. Wider bandwidth operation and multi-band operation are anticipated by extending the known art of conventional Fresnel rings to the DFRs. Increasing the number of rings used to construct a DFR antenna increases the gain, with the upper bound limited often by the largest practical dimensions that can be tolerated for a given application. The maximum theoretical improvement in gain for a single ring is 9.5 dB. Experimental results are within 0.9 dB of this theoretical value. Adding rings increases gain, and theoretically, improvements of 10 to 13 dB above that of the primary antenna gain can be achieved with two- and three-ring versions.

Kennedy, Timothy F.↗

NASA NTRS1984

An operator calculus for surface and volume modeling

The mathematical techniques which form the foundation for most of the surface and volume modeling techniques used in practice are briefly described. An outline of what may be termed an operator calculus for the approximation and interpolation of functions of more than one independent variable is presented. By considering the linear operators associated with bivariate and multivariate interpolation/approximation schemes, it is shown how they can be compounded by operator multiplication and Boolean addition to obtain a distributive lattice of approximation operators. It is then demonstrated via specific examples how this operator calculus leads to practical techniques for sculptured surface and volume modeling.

Gordon, W. J.↗

NASA NTRS1983

Photovoltaic stand-alone modular systems, phase 2

The final hardware and system qualification phase of a two part stand-alone photovoltaic (PV) system development is covered. The final design incorporated modular, power blocks capable of expanding incrementally from 320 watts to twenty kilowatts (PK). The basic power unit (PU) was nominally rated 1.28 kWp. The controls units, power collection buses and main lugs, electrical protection subsystems, power switching, and load management circuits are housed in a common control enclosure. Photo-voltaic modules are electrically connected in a horizontal daisy-chain method via Amp Solarlok plugs mating with compatible connectors installed on the back side of each photovoltaic module. A pair of channel rails accommodate the mounting of the modules into a frameless panel support structure. Foundations are of a unique planter (tub-like) configuration to allow for world-wide deployment without restriction as to types of soil. One battery string capable of supplying approximately 240 ampere hours nominal of carryover power is specified for each basic power unit. Load prioritization and shedding circuits are included to protect critical loads and selectively shed and defer lower priority or noncritical power demands. The baseline system, operating at approximately 2 1/2 PUs (3.2 kW pk.) was installed and deployed. Qualification was successfully complete in March 1983; since that time, the demonstration system has logged approximately 3000 hours of continuous operation under load without major incident.

Naff, G. J.↗

NASA NTRS1977

A theoretical study of the efficiency of the general circulation

The paper examines the problem of explaining the atmospheric efficiency, or equivalently, the rate of generation of available potential energy (APE) by diabatic heating. Attention is focused on determining the maximum possible rate of generation of APE and its accompanying temperature field, which does not require a knowledge of the atmospheric motions leading to temperature distribution. Qualitative and quantitative results indicate that the atmosphere may be operating within approximately a factor of 2 of its maximum efficiency. The general circulation may be operating at nearly its maximum efficiency.

Schulman, L. L.↗

NASA NTRS2014

Designing an Alternate Mission Operations Control Room

The Huntsville Operations Support Center (HOSC) is a multi-project facility that is responsible for 24x7 real-time International Space Station (ISS) payload operations management, integration, and control and has the capability to support small satellite projects and will provide real-time support for SLS launches. The HOSC is a serviceoriented/ highly available operations center for ISS payloads-directly supporting science teams across the world responsible for the payloads. The HOSC is required to endure an annual 2-day power outage event for facility preventive maintenance and safety inspection of the core electro-mechanical systems. While complete system shut-downs are against the grain of a highly available sub-system, the entire facility must be powered down for a weekend for environmental and safety purposes. The consequence of this ground system outage is far reaching: any science performed on ISS during this outage weekend is lost. Engineering efforts were focused to maximize the ISS investment by engineering a suitable solution capable of continuing HOSC services while supporting safety requirements. The HOSC Power Outage Contingency (HPOC) System is a physically diversified compliment of systems capable of providing identified real-time services for the duration of a planned power outage condition from an alternate control room. HPOC was designed to maintain ISS payload operations for approximately three continuous days during planned HOSC power outages and support a local Payload Operations Team, International Partners, as well as remote users from the alternate control room located in another building. This paper presents the HPOC architecture and lessons learned during testing and the planned maiden operational commissioning. Additionally, this paper documents the necessity of an HPOC capability given the unplanned HOSC Facility power outage on April 27th, 2011, as a result of the tornado outbreak that damaged the electrical grid to such a degree that significantly inhibited the Tennessee Valley Authority's ability to transmit electricity throughout the North Alabama region.

Montgomery, Patty↗

NASA NTRS2014

Designing an Alternate Mission Operations Control Room

The Huntsville Operations Support Center (HOSC) is a multi-project facility that is responsible for 24x7 real-time International Space Station (ISS) payload operations management, integration, and control and has the capability to support small satellite projects and will provide real-time support for SLS launches. The HOSC is a service-oriented/ highly available operations center for ISS payloads-directly supporting science teams across the world responsible for the payloads. The HOSC is required to endure an annual 2-day power outage event for facility preventive maintenance and safety inspection of the core electro-mechanical systems. While complete system shut-downs are against the grain of a highly available sub-system, the entire facility must be powered down for a weekend for environmental and safety purposes. The consequence of this ground system outage is far reaching: any science performed on ISS during this outage weekend is lost. Engineering efforts were focused to maximize the ISS investment by engineering a suitable solution capable of continuing HOSC services while supporting safety requirements. The HOSC Power Outage Contingency (HPOC) System is a physically diversified compliment of systems capable of providing identified real-time services for the duration of a planned power outage condition from an alternate control room. HPOC was designed to maintain ISS payload operations for approximately three continuous days during planned HOSC power outages and support a local Payload Operations Team, International Partners, as well as remote users from the alternate control room located in another building.

Montgomery, Patty↗

DOE OSTI2023

Dimension Reduction and Redundancy Removal through Successive Schmidt Decompositions

Quantum computers are believed to have the ability to process huge data sizes, which can be seen in machine learning applications. In these applications, the data, in general, are classical. Therefore, to process them on a quantum computer, there is a need for efficient methods that can be used to map classical data on quantum states in a concise manner. On the other hand, to verify the results of quantum computers and study quantum algorithms, we need to be able to approximate quantum operations into forms that are easier to simulate on classical computers with some errors. Motivated by these needs, in this paper, we study the approximation of matrices and vectors by using their tensor products obtained through successive Schmidt decompositions. We show that data with distributions such as uniform, Poisson, exponential, or similar to these distributions can be approximated by using only a few terms, which can be easily mapped onto quantum circuits. The examples include random data with different distributions, the Gram matrices of iris flower, handwritten digits, 20newsgroup, and labeled faces in the wild. Similarly, some quantum operations, such as quantum Fourier transform and variational quantum circuits with a small depth, may also be approximated with a few terms that are easier to simulate on classical computers. Furthermore, we show how the method can be used to simplify quantum Hamiltonians: In particular, we show the application to randomly generated transverse field Ising model Hamiltonians. The reduced Hamiltonians can be mapped into quantum circuits easily and, therefore, can be simulated more efficiently.

97 MATHEMATICS AND COMPUTING↗